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A López-Escobar theorem for metric structures, and the topological Vaught conjecture

Samuel Coskey, Martino Lupini (2016)

Fundamenta Mathematicae

We show that a version of López-Escobar’s theorem holds in the setting of model theory for metric structures. More precisely, let denote the Urysohn sphere and let Mod(,) be the space of metric -structures supported on . Then for any Iso()-invariant Borel function f: Mod(,) → [0,1], there exists a sentence ϕ of ω ₁ ω such that for all M ∈ Mod(,) we have f ( M ) = ϕ M . This answers a question of Ivanov and Majcher-Iwanow. We prove several consequences, for example every orbit equivalence relation of a Polish group...

A reconstruction theorem for locally moving groups acting on completely metrizable spaces

Edmund Ben-Ami (2010)

Fundamenta Mathematicae

Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category...

Approximate quantities, hyperspaces and metric completeness

Valentín Gregori, Salvador Romaguera (2000)

Bollettino dell'Unione Matematica Italiana

Mostriamo che se X , d è uno spazio metrico completo, allora è completa anche la metrica D , indotta in modo naturale da d sul sottospazio degli insiemi sfocati («fuzzy») di X dati dalle quantità approssimate. Come è ben noto, D è una metrica molto interessante nella teoria dei punti fissi di applicazioni sfocate, poiché permette di ottenere risultati soddisfacenti in questo contesto.

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